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合成材料:力学,计算和应用
ESCI SJR: 0.354 SNIP: 0.655 CiteScore™: 1.2

ISSN 打印: 2152-2057
ISSN 在线: 2152-2073

合成材料:力学,计算和应用

DOI: 10.1615/CompMechComputApplIntJ.v1.i3.30
pages 245-265

AVERAGING OF THE HEAT CONDUCTION EQUATIONS WITH ACCOUNT FOR THE CONVECTIVE MECHANISM OF HEAT TRANSFER

A. N. Vlasov
Institute of Applied Mechanics, Russian Academy of Sciences, 7 Leningradsky Ave., Moscow, 125040, Russian Federation
Viktoria L. Savatorova
Central Connecticut State University, New Britain, CT
Alexey Talonov
UNLV, MEPhI

ABSTRACT

Within the framework of asymptotic averaging of differential equations with rapidly oscillating coefficients the asymptotics of the solution of the joint problem of heat conduction and filtration for inhomogeneous media with a periodic structure is being built (up to the terms of the second order of smallness), which allows one to take into account convective heat transfer. The problem is solved in nonlinear statement when the dependence of thermophysical and filtration properties on temperature is taken into consideration. General equations to describe the processes of heat conduction with account for conductive and convective mechanisms of heat transfer, as well as for the possibility of phase transitions are obtained. The solution of the problem on the propagation of heat on heating of a semi-infinite laminated medium has been solved with account for the processes of phase transitions and subsequent filtration of a liquid phase.

REFERENCES

  1. Bakhvalov, N. S. and Panasenko, G. P., Osrednenie protsessov v periodicheskikh sredakh (Averaging of the Processes in Periodic Media).

  2. Landau, L. D. and Lifshits, E. M., Girdodinamika (Hydrodynamics).

  3. Loitsyanskii, L. G., Mekhanika zhidkosti i gaza (Mechanics of Liquids and Gases).

  4. Nikolaevskii, V. N., Mekhanika poristykh i treshchinovatykh sred (Mechanics of Porous and Fissured Media).

  5. Vlasov, A. N., Savatorova, V. L., and Talonov, A. V., Use of the method of asymptotic averaging for solving the problems of heat conduction with phase transitions.

  6. Kapranov, V. E. and Perlshtein, G. Z., Investigation of the transverse scattering of heat in water-saturated filtering grounds.


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